MathDB
Problems
Contests
National and Regional Contests
Taiwan Contests
TST Round 2
2019 Taiwan TST Round 2
1
Almost Symmetric Inequality
Almost Symmetric Inequality
Source: 2019 Taiwan TST Round 2
April 1, 2020
inequalities
algebra
High school olympiad
Problem Statement
Prove that for any positive reals
a
,
b
,
c
,
d
a,b,c,d
a
,
b
,
c
,
d
with
a
+
b
+
c
+
d
=
4
a+b+c+d = 4
a
+
b
+
c
+
d
=
4
, we have
∑
c
y
c
3
a
3
a
2
+
a
b
+
b
2
+
∑
c
y
c
2
a
b
a
+
b
≥
8
\sum\limits_{cyc}{\frac{3a^3}{a^2+ab+b^2}}+\sum\limits_{cyc}{\frac{2ab}{a+b}} \ge 8
cyc
∑
a
2
+
ab
+
b
2
3
a
3
+
cyc
∑
a
+
b
2
ab
≥
8
Back to Problems
View on AoPS